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feat(polytime): report a failed certificate subterm - #1738

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feat/polytime-failure-hint-20261030

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@SamuelSchlesinger SamuelSchlesinger commented Oct 30, 2026 •

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When compositional search fails, polytime currently loses the backend’s useful subterm diagnostic in the outer search error. This retains the first already-rendered backend report in an invocation-local reference and appends it only when the outer tactic ends in ordinary failure. Nested calls receive separate collectors, and the environment is restored after success or exceptional exit. Search order, budgets and the number of search attempts are unchanged; heartbeat, recursion-limit and interrupt exceptions keep their original meaning.

The message describes one failed search route, not a proof of noncomputability or a unique root cause. Only rendered strings are retained, so variables from closed backend telescopes do not escape. New ordinary-import regressions exercise missing callbacks, captured parameters, supplied-certificate success, repeated calls and recovery. A small internal companion checks nested collectors, cleanup and the original Lean resource/interrupt exception constructors. The tactic and both new test modules compile with warnings as errors; the existing PolyTimeContracts, PolyTimePlainDriver and ProgramCertificateDiagnostics checks also pass, including rebuilt PPT/signature/MAC clients. Python source hygiene and diff checks pass. Focused checks use pinned Lean and source-matched read-only artifacts with isolated outputs; canonical gates run in hosted CI. No mathematical statements or selected abstracts change.

Implements the separate diagnostics slice agreed in #1155 after #1225; the broader automation objective remains open. Current source/API review records the preserved implementation and validated formatting fix. All six local and canonical hosted gates pass. The integration record records actual landing and main publication status.

AI assistance: implemented and locally checked by OpenAI Codex agents complexitylib-incremental-20261030 / semantic_design; no human review is implied. Codex coordinator /root performed the validated test-formatting fix and current source/API review; the feature implementation is preserved.

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Independent source review by Codex worker agent /root/review_proofs_tactic, relayed by the author for 76c7eda15dd9c8b63837c90a82d58c9b28cf967f: Approve; no changes requested.

The reviewer checked invocation/nesting lifetime, backtracking through the shared local reference, eagerly rendered FunProp strings, and restoration on all exits against the pinned Lean/Mathlib implementations. Ordinary terminal errors retain their original reference/message plus one search-route note; heartbeat, recursion-limit and interrupt exceptions bypass decoration. No new search, rule order, step budget or success path was added. The ordinary-import and internal cleanup/exception regressions and existing PolyTimeContracts have matching warning-strict receipts with empty logs.

I verified that the published commit’s complete Git tree equals the reviewed local tree. The reviewer did not participate in implementation/design and made no edits. This is agent source approval, not human or platform approval; canonical CI on the final revision remains required before integration.

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Non-author coordinator /root: source review is in progress. Canonical CI's strict library build passed; its test failure is confined to two 100-column style warnings in PolyTimeFailureHintScope.lean (lines 66 and 70), rather than a diagnostic/scope assertion failure. I will wrap those two lines as a validated coordinator fix, preserving the tactic, test terms and resource limits, then validate and review the resulting revision. No unchanged CI rerun or linter suppression.

Fix the two canonical strict-test long-line warnings. All non-whitespace tokens and string literals are unchanged; tactic behavior, test assertions and resource limits are preserved. AI assistance: non-author Codex coordinator /root under the validated coordinator-fix rule.

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Non-author coordinator /root: Approve f07988cf4646084bac92c0a70cc7f0c433f85cff under the validated coordinator-fix rule. I inspected the complete feature and reused the scoped source review. The only fix on top is two line wraps in the scope test: every non-whitespace token and string literal is unchanged. No tactic, assertion, rule order or resource budget changed.

The invocation-local reference survives search backtracking while withEnv restores the surrounding collector; nested invocations get fresh collectors. Reports retain rendered strings rather than escaped expressions. Pinned Lean's ordinary Core.tryCatch filters resource and interrupt exceptions, so those retain their original constructors/messages; the new controls exercise these exits and cleanup. Ordinary failures receive one attempted-route hint, not a noncomputability claim.

All six local gates pass on the exact clean revision, including both new regressions and existing clients. Source hygiene, the compiled ratchet and full own-layer changed-file checks (one library module, two tests) pass. No selected abstract or mathematical resource statement changes. The normal guarded push preserves the author's feature; fresh current-head CI is required before queueing. I retain integration ownership. Agent review under the shared-account rule, not human/platform approval.

@SamuelSchlesinger
SamuelSchlesinger added this pull request to the merge queue Oct 30, 2026
Merged via the queue into main with commit 9acffb0 Oct 30, 2026
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SamuelSchlesinger commented Oct 30, 2026 •

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Coordinator /root: integration and usable-cache follow-through complete. Landed at 9acffb0706ab25d05eb12693547990d6a89a550d on main, verified through the merged PR and direct Git branch. The exact merge-group run is terminal success and checks out that commit. The source/API review and validated formatting fix remain the review record.

Main CI, attempt 1, is terminal success. Its finalized log verifies the exact checkout, all six gates, restoration from merge-group run 41100293815 attempt 1, and publication at 18:33:12 UTC. The job API omitted individual steps, so this uses the complete log plus successful run/job conclusions. Ordinary validation ran after restoration.

The public revision mapping returns GET 200: 180,958 bytes and 4,021 unique pairs. Reusing the verified e596 baseline, all three new artifact references return HEAD 200; no artifact bodies were downloaded. This same consumer covers the landed #1775 prefix. The diagnostics slice is complete; broader #1155 automation remains open. Agent review/integration, not human approval.

orbitingflea pushed a commit to orbitingflea/complexitylib2 that referenced this pull request Oct 30, 2026
…lib-community#1734)

* feat(polytime): certify fixed-list flatMap and filtered templates

* feat(LogSpace): configuration matrix of fair-coin machines (cslib-community#1665)

* feat(LogSpace): configuration matrix of fair-coin machines (cslib-community#474)

Coin-driven transition matrices (Foundations) and, for a fair-coin
machine on a closed set of views, the acceptance probability as an entry
of N^t e, of the substochastic sum, and of (1 - S/2)^-1 e. BPL through
polynomial-size configuration matrices.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* fix(LogSpace): Hoza citation scope; export reachability and nilpotency for BPL

Hoza Section 4.3 states BPSPACE(S) ⊆ DSPACE(S^2); the inverse picture is
Section 3.2, and BPL ⊆ P is no longer attributed to it.
exists_configMatrix_of_mem_BPL now also exports reachability of V, the
polynomial halting time and S^(T+1) = 0.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
Co-authored-by: Codex integration coordinator <codex-integration@users.noreply.github.com>

* ci(guide): check examples when library APIs change (cslib-community#1731)

* refactor(computability): decouple native certificate combinators from RAM models (cslib-community#1733)

* test(comparator): add independently stated proof checks (cslib-community#1729)

Add reviewed reduction, circuit, polynomial-time, and SAT contracts with solution wrappers, a sandboxed comparator runner, and a changed-statement negative control. Keep generated challenge placeholders outside ordinary builds and import aggregation.

Document the trusted inputs and sandbox requirements, and run the selected checks in dedicated CI on library or harness changes.

AI-assisted implementation and scoped independent agent review using OpenAI Codex.

* perf(ci): prepare controlled cache-handoff measurement (cslib-community#1744)

* perf(ci): prepare dormant cache handoff measurements

Add temporary, default-disabled prospective sampling and same-runner cache-isolation fixtures for cslib-community#1728. Preserve the existing restore contract, all required validation and main-only cache publication. No experiment or activation is performed; cslib-community#1197 remains open for the controlled net-cost decision.

AI assistance: OpenAI Codex implemented the private driver, workflow wiring, isolation/budget/failure tests and execution protocol. Python and configuration checks pass; this checkpoint precedes serialized full validation and independent CI/provenance review. No Lean source or selected abstract changes.

* fix(ci): apply measurement deadlines to arm resets

Carry the paired work deadline through copy and manifest checks, preserve deadline-free recovery, and check failure isolation. Clarify filesystem granularity and cleanup limits. AI assistance: Codex coordinator /root self-review of the delegated cslib-community#1728 implementation.

* refactor(Machines): plain polynomial-time tape, configuration and breadth-first search rules (cslib-community#1670)

* refactor(Machines): plain polynomial-time tape, configuration and NL ⊆ P search rules (cslib-community#862)

Plain ComputableInPolyTime rules for stack and bidirectional tapes, finite
configurations (observations, fixed actions, initialization), list tail and
emptiness, and the breadth-first search of Reachability (insertNew, expand,
viewSucc), proved without the tidy calculus. The closed tidy tape and
configuration rules are derived from the plain ones; the three tidy search
rules are replaced (tidy baseline 704 -> 701).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* style(Machines): use canonical tidy-baseline serialization

Use the repository baseline_text formatter after the metadata-only union. Parsed entries remain identical at 690. The exact failing committed-baseline Python test passes without Lean or local dependencies.

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
Co-authored-by: Codex integration coordinator <codex-integration@users.noreply.github.com>

* refactor(crypto): separate commitment interfaces from Naor construction (cslib-community#1737)

* test(cache): isolate measurement fixtures from host free space (cslib-community#1755)

Mock ample default disk capacity with cleanup for tiny fixture copies. Keep the explicit insufficient-space override and all production resource checks unchanged. Found on a constrained host while validating cslib-community#1730; tracked separately in cslib-community#1753. No library, abstract or renderer impact. AI assistance: Codex worker /root/mathlib_cache_retry_1730.

* feat(TM): add native counted block transfers (cslib-community#1735)

Provide copy and source-erasing modes for local blocks, including physical
blanks, with exact native execution, first-halting time and visited-space
proofs. Test arbitrary offsets, populated tapes and zero-length transfer.

This is a bounded prerequisite for buffered simulation in cslib-community#800; buffer
layout, counter preparation, scheduling and amortization remain open.

Co-authored-by: ChatGPT <noreply@openai.com>

* feat(logspace): add polynomial cutoffs with Lipschitz fourth roots (cslib-community#1743)

* feat: add rational polynomial switches with Lipschitz fourth roots

Supply a computable rational degree-seven transition and its rescaling, with
real endpoint, monotonicity, and value/complement fourth-root Lipschitz laws.
Exact rational cast lemmas connect the arithmetic definitions to the real
analysis. Concrete tests cover interior values, affine rescaling, clamping,
equal endpoints, and root perturbations across both transition boundaries.

This advances issue cslib-community#1721's fourth-moment route. The pinned primary source
OpenAI2026LogSpace, atoms.tex Section 5.1 at revision 7ef5c0cc, uses the same
normalized-integral construction with s = 8. This implementation specializes
it to s = 4 and does not claim eighth-root regularity, complete hierarchy
admissibility, or machine resource bounds. No OpenAI Lean was consulted.

Validation on base 2d1638c with the two added files: both modules compile
under the repository's Lean options with warnings as errors using isolated
temporary outputs and read-only existing dependencies; focused
check_hygiene.py --check-simp and git diff --cached --check pass. The final
documentation-only wording change was inspected after those builds. Full
repository integration gates and independent review remain for coordinator
integration; no aggregate file has been edited.

Authored by worker codex-logspace-polynomial-cutoffs-20261030 with ChatGPT.

Independent agent source/API review: codex-compression-iteration-20261030 approved source a6967d13aafee47ae16b61ac2b12f533426f9971 and freshly compiled both files. Publication adds only the generated aggregate import. Integrated strict module/test builds, hygiene and whitespace checks pass. Full gates run in PR CI.

* fix(logspace): keep cutoff aggregate independent of compression

Remove three aggregate imports that came from untracked source copies during integration. The polynomial switch module and tests are unchanged. Validate import targets against the committed Git tree before publication.

* feat(LogSpace): Savitch's theorem in space log² n, NL and RL in DSPACE(log² n) (cslib-community#474) (cslib-community#1671)

* refactor(LogSpace): plain statements for query machines and compact configuration graphs (cslib-community#474, cslib-community#862)

State the space theorems of query machines (`Turing.QueryMachine.computableInSpace`,
`.computableInLogSpace`) with plain `ComputableInSpace` hypotheses, and restate the compact
configuration-graph routines (`ConfigurationGraph.Radix`, `ConfigurationGraph.Routines`) in the
plain `ComputableInSpace` budget calculus of `InSpaceLib`, whose rules they already mirrored.
The query-machine simulation still converts internally; the radix and graph routines are now
proved without tidy computability. Clients (counter programs, inductive counting, the
configuration-graph test) adapt at their call sites. The public tidy surface drops by 11
statements (704 -> 693).

This is the plain dependency for the log-squared Savitch simulation of cslib-community#474 M3.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* feat(LogSpace): Savitch's theorem in space log² n, NL and RL in DSPACE(log² n) (cslib-community#474)

Prove `NL ⊆ DSPACE(log² n)` [Savitch1970] and, through `RL ⊆ NL`, `RL ⊆ DSPACE(log² n)`
(milestone M3 of cslib-community#474).

The machine-level result `Turing.MultiTapeNTM.exists_decidableInTimeAndSpace_log_sq` simulates
a recognizer within space `c * (log₂ n + 1)` by a deterministic query machine
(`Turing.MultiTapeNTM.LogSquareSavitch.machine`) within space `O((log₂ n + 1) ^ 2)`. The machine
counts the input, fixes the radix `(n + 2) ^ D` of the compact configuration graph, and runs the
existing explicit-stack midpoint recursion (`Cslib.Reachability.Savitch.step`) on its vertices as
words of `W = O(log n)` bits, with a sink word reached from accepting halted vertices. The edge
test reads the one input bit at the source's input head, so the input is never copied. The
class-level statements live in `Classes/LogSpace/Savitch.lean`.

The proofs use only plain statements: the plain query-machine and configuration-graph routines
of the previous commit, `Savitch.computableInO_roundStep`, the plain `ComputableInSpace` budget
calculus and finite transducers. The run invariant of Savitch's machine
(`Savitch.Invariant`, `invariant_iterate`, `length_encState_le`) becomes public for the size
bound. Adds bibliography entries Savitch1970 and Hoza2022.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* refactor(LogSpace): reuse existing transducers in the log-squared Savitch simulation (cslib-community#474)

Address the review of cslib-community#1671:
- the power of two from unary uses `ComputableInDegree.two_pow_length encUnary` instead of a
  copy of `Turing.MultiTapeTM.twoPowT`;
- `isSome_inSpace` is `ComputableInDegree.isSome` instead of a new transducer;
- the all-ones test reuses `Cslib.Reachability.Savitch.allT`, now public, instead of a copy.

The fixed-width words move to `Encodings/Nat/Words.lean` as `Turing.MultiTapeTM.bitsOfWidth`
with `length_bitsOfWidth`, `ofBits_cons`, `ofBits_bitsOfWidth`, `bits_add_two_pow`,
`dropLast_bits_add_two_pow` and `ofBits_replicate_true`; the unused `pad_zero` is dropped.
`transducer_inSpace` and `budget_some` stay local, since `InSpaceLib` is edited by open PRs.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* refactor(LogSpace): reuse lowBits and existing word certificates in log-squared Savitch (cslib-community#474)

Address the delta review of cslib-community#1671:
- the fixed-width words are `Cslib.BitString.lowBits`; `bitsOfWidth`, `length_bitsOfWidth`,
  `ofBits_bitsOfWidth`, `ofBits_cons` and `ofBits_replicate_true` are removed in favour of
  `length_lowBits`, `lsbValue_lowBits`, `lsbValue_eq_foldr_bit` and `lsbValue_replicate_true`;
- `bits_add_two_pow` and `dropLast_bits_add_two_pow` in `Encodings/Nat/Words.lean` are stated
  with `lowBits`, proved from `Nat.bits_foldr_bit_one`;
- further duplicates found in a self-check: the unary length transducer is replaced by
  `ComputableInO.lengthUnary`, and the local `budget_some` by `ComputableInDegree.optionSome`.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* docs(LogSpace): cite Sipser's sublinear extension of Savitch's theorem (cslib-community#474)

Theorem 8.5 assumes f(n) >= n. The sublinear statement is the final
paragraph of Section 8.4 (3rd ed., p. 351). Map its read-only-input
convention to the compact configuration graph and query machine, and
distinguish the nonhalting-recognizer and encoded-instance strengthenings.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* chore: regenerate Savitch aggregate import order

Apply the actual mk_all output after integration. Only the aggregate ordering changes; reviewed theorem, definition and proof text is unchanged. AI assistance: Codex coordinator /root.

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
Co-authored-by: Samuel Giuseppe Schlesinger <sgschlesinger@gmail.com>

* feat(logspace): bound source release through correction atoms (cslib-community#1742)

* feat(logspace): bound source release through correction atoms

Prove the finite double-counting inequality in the source-domain part of
OpenAI2026LogSpace Lemma 7.3 and its exact K * (f / u) cost in integrated
table and vector norms. Instantiate both statements with correctionAtom,
discharging the incoming-degree bound from its incoming gate. Shared
environment dependence remains unrestricted; the right error is common
to every old source.

Expose the rowNormPow and vertexNormPow bodies for this downstream
mathematical consumer. No definitions or theorem statements change.

Validation against base 2d1638c: direct Lean elaboration with project
options and warnings as errors passed for RootMetric, SourceRelease,
ComplexityTests.SourceRelease and the existing ComplexityTests.RootMetric
(covering AtomCutoffs and RootError). Outputs were private; dependencies
were read-only. Hygiene with --check-simp and git diff --check passed.
The changed-file lint requires the absent ComplexityAbstracts.ilean root
in this source-only worktree, so its full check and project-wide gates
remain for CI. Aggregate imports are left to the integrating coordinator.

Tests include a sharp f / u = 2 example with correlated support and error,
and a correction atom with a verified nonzero edge. This proves the
source-release inequality, not the remaining scale comparisons, true
sample means, recursive estimator or native BPL-to-L machine.

AI assistance: OpenAI Codex implemented and checked this change.

Independent agent source/API review: codex-logspace-polynomial-cutoffs-20261030 approved final43118874cf98b42ae1ed3bc776a6c7e6fd9f4d6d. Publication adds only the generated aggregate import. Integrated strict builds of SourceRelease, its tests and existing RootMetric tests pass. Full gates run in PR CI.

* fix(logspace): keep source-release aggregate independent of compression

Remove three stray aggregate imports introduced during local integration. Source-release proofs, APIs and tests remain unchanged. The committed import graph is now checked before publication.

* feat(logspace): prove the local row compression lemma (cslib-community#1736)

The Phase 4 estimator needs to retain only a bounded list of exceptions
without losing stability when that list changes. Formalize the native
two-coordinate compression update of OpenAI2026LogSpace Section 8.2,
equations (8.5)-(8.6), and all conclusions of Lemma 8.1.

Prove small-entry replacement, signed large-entry preservation,
coordinatewise interpolation, monotone defaults, strict candidate capacity
and containment, and uniform 28-Lipschitz stability. Also prove the local
6u change bound used by the subsequent preloss argument. Add concrete tests
of partial clipping, signed values, positive-default padding, empty rows,
candidate selection and perturbations.

This advances cslib-community#1721 and cslib-community#1444. Iterated propagation and its slack conversion
(8.7), rarity estimates, recursive estimation and machine-space realization
remain open. No selected formal abstract or roadmap endpoint changes.

Validation on Lean v4.36.0-rc2, based on main ef811c8:
- Strict focused build of the module and concrete tests passed.
- scripts/check.sh passed all six gates: strict full build, mk_all check,
  strict full tests (including the global axiom audit), lint, lint-style,
  and checkInitImports.
- check_changed_files.py, check_tidy_surface.py, and check_hygiene.py passed.
- Focused hygiene with --check-simp and git diff --check passed.

Independent non-author review: Codex agent /root/compression_review approved
source tree e70d93b, including primary-source
correspondence, APIs, boundary cases, tests and the one-step change bound.
No requested fixes remain. This is agent review, not human approval.

Worker: codex-row-compression-20261030, branch feat/logspace-compression-update.
AI assistance: OpenAI Codex implementation and independent Codex review.

* refactor(encodings): retain degree bounds in option decoders (cslib-community#1732)

* ci(cache): retry partial Mathlib downloads in place (cslib-community#1775)

Share three bounded non-forced cache-get attempts between local bootstrap, Lean CI and API docs. Retain completed archives and the lean-action/local URL-default distinction; only cache failures fall back to strict compilation. Docs reuse the existing missing-only Complexity helper. Add partial-download, retry, timeout, URL, checkout and strict-failure regressions. No Lean, abstract or renderer-source impact. AI assistance: Codex worker /root/mathlib_cache_retry_1730 for cslib-community#1730.

* feat(polytime): report a failed certificate subterm (cslib-community#1738)

* feat(polytime): report a failed certificate subterm

* style(tests): wrap polynomial-time hint controls

Fix the two canonical strict-test long-line warnings. All non-whitespace tokens and string literals are unchanged; tactic behavior, test assertions and resource limits are preserved. AI assistance: non-author Codex coordinator /root under the validated coordinator-fix rule.

* refactor(Universal): dedupe encodings and extract proof fragments in Universal/Complexity (cslib-community#1769)

Move encSign and encUnit to Encodings/Bool (replacing the identical encMove
and a test-local encUnit), move the encInt successor/predecessor length bounds
next to length_encInt, and extract repeated size arguments of the step
complexity proof into lemmas.

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

* feat(BigO): plain findWith, filterWith and mapWith (cslib-community#1773)

Move the private plain findWith/filterWith of SparseMemory/Turing to a public
module Complexity/BigO/Lists and add the plain mapWith, so that clients of the
tidy list combinators can migrate to the plain calculus.

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

* doc(roadmap): expand algorithms and complexity coverage (cslib-community#1768)

* feat(descriptive): compile ordered FO and prove parity nondefinability (cslib-community#1739)

Compile canonical ordered FO sentences to constant-depth polynomial-size formulas over the original relation atoms, including genuine numeric constants. Use the compiler with the existing AC0 parity lower bound to prove nondefinability in Ordered.Definable. Add concrete compiler and query regression examples.

Validated the two new modules, their existing FirstOrder dependencies, and OrderedFirstOrderCircuits with Lean 4.36.0-rc2, autoImplicit=false and warnings as errors. Full repository gates are delegated to hosted CI. AI assistance: OpenAI ChatGPT/Codex authoring.

Published through the GitHub connector. Source tree is identical to locally validated and independently reviewed commit 46ef7adc52337bcb69283196dc5ca3d2611a99d7.

* feat(descriptive): prove the ordered Fagin characterization (cslib-community#1761)

* feat(MCSP): prove formula magnification for subexponential parameters (cslib-community#1760)

Complete the asymptotic step of Oliveira-Santhanam Theorem 17(iii),
including the real N^(1+epsilon) bound, using the existing SuccinctMCSP
reduction and NP membership. Add reusable logarithmic subexponential
growth bounds and concrete regression tests.

Related to cslib-community#798. Theorem 17(ii), Theorem 5 asymptotics and the efficient
anti-checker generator remain open.

Co-authored-by: ChatGPT <noreply@openai.com>

* feat(data-structures): support ordered-set deletion and minimum extraction (cslib-community#1756)

Connect verified search-tree deletion to the shared typed ordered-set interface and adaptive-client correctness/resource certificates. Add extractMin with complete result, final-state, history and cardinality theorems, plus concrete deleting-client regressions.

Pinned Lean 4.36.0-rc2 checks pass without warnings for all changed modules and three affected test modules. Source hygiene and diff checks pass; full repository validation runs in hosted CI before integration. Costs remain internal-node visits, excluding allocation, comparison implementation and pure client evaluation.

AI assistance: OpenAI ChatGPT implementation by /root and /root/data_structures_survey; independent non-authoring API/correctness review by /root/ordered_set_review approved exact tree e18fa61 with no findings. This is AI review, not maintainer approval.

* feat(logspace): iterate row compression and bound accumulated loss (cslib-community#1740)

* feat(logspace): prove the local row compression lemma

The Phase 4 estimator needs to retain only a bounded list of exceptions
without losing stability when that list changes. Formalize the native
two-coordinate compression update of OpenAI2026LogSpace Section 8.2,
equations (8.5)-(8.6), and all conclusions of Lemma 8.1.

Prove small-entry replacement, signed large-entry preservation,
coordinatewise interpolation, monotone defaults, strict candidate capacity
and containment, and uniform 28-Lipschitz stability. Also prove the local
6u change bound used by the subsequent preloss argument. Add concrete tests
of partial clipping, signed values, positive-default padding, empty rows,
candidate selection and perturbations.

This advances cslib-community#1721 and cslib-community#1444. Iterated propagation and its slack conversion
(8.7), rarity estimates, recursive estimation and machine-space realization
remain open. No selected formal abstract or roadmap endpoint changes.

Validation on Lean v4.36.0-rc2, based on main ef811c8:
- Strict focused build of the module and concrete tests passed.
- scripts/check.sh passed all six gates: strict full build, mk_all check,
  strict full tests (including the global axiom audit), lint, lint-style,
  and checkInitImports.
- check_changed_files.py, check_tidy_surface.py, and check_hygiene.py passed.
- Focused hygiene with --check-simp and git diff --check passed.

Independent non-author review: Codex agent /root/compression_review approved
source tree e70d93b, including primary-source
correspondence, APIs, boundary cases, tests and the one-step change bound.
No requested fixes remain. This is agent review, not human approval.

Worker: codex-row-compression-20261030, branch feat/logspace-compression-update.
AI assistance: OpenAI Codex implementation and independent Codex review.

* feat(logspace): iterate row compression and bound accumulated loss

Add concrete increment-and-compression states and schedules. Prove width-independent 28^j propagation, exact restarts, a fifth-power slack bound under an explicit group-count condition, and accumulated row/default loss before overflow. This establishes the update-only part of OpenAI2026LogSpace (8.7) and the unweighted part of Lemma 8.2; weighted preloss and the final root functions remain separate.

Validation on base c3f7a58: direct Lean 4.36.0-rc2 checks of both new modules with project options passed without diagnostics, using isolated output files and the parent checkout dependencies read-only. Concrete tests cover a two-group nonzero-loss execution, satisfied no-overflow bounds, an actual overflow after lowering capacity, and distinct initial-state perturbations. Focused proof hygiene including --check-simp and git diff --check passed. Aggregate regeneration and full project gates are delegated to integration.

AI assistance: ChatGPT implemented and checked these proofs as worker codex-compression-iteration-20261030.


Independent agent source/API review: codex-source-release-20261030 approved the library and tests at 7d08e44bbdb626b74adaa9c4d63e07faa28ce525. Publication adds only the generated aggregate import. Integrated targeted build, tests, aggregate check, hygiene and whitespace checks pass. Full gates run in PR CI.

* feat(logspace): certify local fair-coin configuration counts (cslib-community#1763)

Read each fixed-coin edge of the compact configuration graph and add the
two contributions, preserving multiplicity when the successors coincide.
Certify the count and live-count routines with the existing native space
combinators. Prove normalized tape and canonical-view ID injectivity, then
identify the queries with actual configMatrix/liveConfigMatrix entries.
Reachable-logspace corollaries derive the representation conditions from
RunsInSpace at the prescribed polynomial radix.

Tests use actual zero-tape machines and reachable views to distinguish
zero, one and two coin branches, absorbing and zero-live halted rows,
invalid IDs, and the exact binary argument space certificate.

Validation on base df2279f plus this four-file diff: all three modules and
the test pass direct Lean 4.36.0-rc2 checks with warningAsError=true and
repository linter options, with no diagnostics. Focused hygiene
--check-simp and staged git diff --check pass. Outputs are isolated and
shared compiled dependencies are read-only. Aggregate wiring, independent
review and the full CI gates are left to the coordinating integration.

This is local matrix access, not bounded vertex enumeration, time layering,
an estimator implementation or the BPL subset L endpoint. No selected
abstract or catalogue impact. AI assistance: ChatGPT (GPT-6 Astra), worker
codex-logspace-coin-multiplicity-20261030, wrote and validated these files.

Independent non-author source/API review by compression_review approved exact source revision be84b9de9d7de13f0d99a3ceb54649ef57f9f7d2, including native resource certificates and exact configuration-matrix bridges, with no findings. Reviewed source files are unchanged after integration onto updated main.
Integrated strict source/test builds, tracked aggregate check, whitespace and committed import checks pass. Full integration gates run in PR CI.

---------

Co-authored-by: chris-ai1 <chris-ai1@catch.exinto.de>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
Co-authored-by: Codex integration coordinator <codex-integration@users.noreply.github.com>
Co-authored-by: ChatGPT <noreply@openai.com>
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